I'm not going to comment about anything else in this thread (agree with some and disagree with some), but the bolded is incorrect on a purely mathematical level. The probability of ending up with exactly $5500 in our roll in this instance would be (100C50)/2^100, or 100!/[(50!)^2 * 2^100]. A crude estimate puts this at roughly 8% (someone else can double-check me here).

Sorry, I shouldn't have used the word "exactly". Look at the next sentence I wrote though. The point was you'd end up near $5500.

So when you say "it's only +EV by $5. I'll fold to reduce variance" realize that over the long run these small mistakes can add up. In my hypothetical example, after 100 hands on average I'll have $500 more than those who are folding to "reduce variance".

Come on, you're always posting these one liners with no justification. We need to know the why. We all need to put in a bit of effort if we want these forums to grow.

1. What parts did you disagree with ITT?
2. Why did you disagree with them?
3. What is the widest range of statement you would continue to disagree with after a 4 page debate?
4. Given your continued disagreement range in 3, would it have been better to fold pre (not entered the thread at all) or three bet (been more expansice in your first post)?
5. Which parts of the thread did you agree with?
6 Why did you agree with them?
7. Do you have mathematical models to back up 2 and 6, as in your excellent OP, or are we expected to see one good maths model then just believe the rest must be right?
8. Why are apples not triangular?

Thanks in advance.

But that's not really true either in the sense that I think you mean it. What is actually true is that the average of all possible scenarios, assuming the ability to have negative money, is that you end up with $5500. In other words, for every scenario you could end up with $4280, there's an equal chance you end up with $6720. Both of these are almost (but not quite) equally as likely to happen as $5500, by the way (probability (100C49)/2^100).

The following is also true: pick some positive integer X and say "I want to be within X times $1220 of $5500". As X increases, the probability that this happens increases rapidly.

EDIT: OK, quesuerte has a point, I'll post responses to his questions soon.

I suck. Sorry, CMV, I was only joking, thought you were Setsy for some reason, ignore my post.

Sorry twice in one thread, WTF is going on here?

In a cash game AK should be played cautiously preflop... opening, 3-betting, maybe even a possible 4-bet to loose players raising/3betting often pre is fine, but I definitely don't like getting it all in pre with AK, even suited, in a cash game.... Only thing you beat is AQ and only a bad player will play all in pre with that hand in a cash game.

Ok say I have a roll of 3k and someone offers me a 50/50 flip 330 if i win 300 if I lose.


I have 10 minimum flips.

After 10 flips I win 3(990) and lose 7($2.1k) = $1890 left.

Do I keep flipping? surely Ill go on heater soon this is +ev with infinite flips but with such a small roll EV might not not hit for another 100 flip

Now if I had a 3k roll and someone offered me 50/50 flip +$33 if I win -$30 if i lose

100 minimum flips variance is a lot less and id take the flip every time.


Also when I bet with hands like QJs and 3bet people I do it because I honestly believe I have >70% chance of winning the hand. Lots of people are fit or fold and fold flop and wont make plays. Yes some go wrong but I definitely win >50% of the hands I raise easily.

I used QQ and an open AK because its reps a flip it could be a coin or w/e its kinda irrelevant.

Ive only been playing live for 181 hours logged current win is $42p/h and I think where I play I can keep it above $30 at 2/4.

Anyways cool discussion

grunch
Being a small favorite is +EV. With that said, pushing small edges increases both profit and swings. If you are adverse to swings the profit from these small edges may not be the correct strategy for you, If you are underrolled (as you state you are) then this may again not be the correct strategy.
The 2/5 games I play are really juicy and there is rarely a lack of better opportunities. I try to avoud the flips (unless there is dead money in addition to the 50:50) with the following exception.

If I am running dry / card dead and develop a super nitty table image then flipping (especially vs a short stack) improves your metagame profitability for later in the session for low risk and a high visability activity.

This is probably going to lead to a long, pointless discussion but your frequency estimations are horrendous IMO. In the QJs thread I posted you raised a bunch of limpers to 5X. Nobody is winning this pot >70% of the time. But the point is this is massively increasing your variance, which you claim to want to avoid. The pot ends up being 5 way with an SPR of about 3. You are getting your stack in with a draw here loads and loads, you are making big cbets and getting committed in huge pots. It doesn't matter how bad or fit fold your opponents are, taking small equity edges and playing large pots is way, way more important to your standard deviation that AK, QQ spots.

This is not to criticize those plays. But you seem to misunderstand where variance comes from and how small edges are. Also the percentage of pots you win is not important. It is the size of the bets, pots and your edge.

This is cash. If you lose your flip, you can just buy back in. You don't have to only take ++EV spots, you can take ALL +EV spots.

I was just discussing this with Greg Raymer last night (very thinly veiled brag) and he brought up this article by Matt Matros about needing to push thin edges even in the first hand of a main event style tournament that uses a very similar hypothetical. http://www.cardplayer.com/cardplayer...or-not-to-flip

And that is in a tournament when losing a flip means that you're out and talking about a pot with no dead money. In your OP, this is 100% a snap every time. If you can't afford the damage of losing three flips in a row, you are significantly under-rolled, either actually or mentally.

Ty Garick. You're the first person so far to basically agree with what I said. This is basically exactly what I said.

I don't think CallMeVernon was disagreeing with you're thoughts on EV, just your thoughts on risk-of-ruin.

+EV can still run a significant risk-or-ruin (ROR) with a small bankroll,a s the long run can be longer than you think. I've known someone to be 15 buy-ins below EV before. It's not common, but I bet that it's not even super exceptionable by statistical standards.

That said, if I had >10BI at the level I was playing, I would snap this scenario every time. If I lose my roll doing it, I'll build my roll back mowing lawns, because the Sklansky-buck profit is there, and that pays off in the long run.

Not even that. I was just correcting the math. If the argument is good, we should be able to make it without bad math. (Also, in my experience a lot of gamblers don't really understand what "the long run" means mathematically, though I think that's mostly incidental to the topic.)

Personally I think that in the example hand in the OP I would be calling every time. If I lose, I reload for another $300 and take this hypothetical "better spot" later with my 2nd (or 3rd) buy-in. If I win, I get to play $650 deep, which I want. Then maybe I can win more when I find my "better spot". It's that simple.

The only times I would ever fold a marginally +EV spot like this are:

1) If I'm gambling for deep stacks and I would not be able to reload to the same amount I had before (or close to it). For example, I might (might) choose not to flip for $600 stacks if the buy-in is capped at $300 but 3 other players at this table have $600-800 and I want to stay deep with them. (On the other hand, if I have even a slight edge and the guy offering me the flip is one of my targets, I usually flip even then.)

2) If I think the mental toll of losing would cause me to play worse in future hands.

Even in these spots, I will almost always still flip if there's a lot of dead money in there, as quesuerte has said also.

Now, that being said, I also believe that a lot of the time, people rationalize bad calls by saying things like "it's marginally +EV against this guy's range as a whole" when we aren't sure the range includes the weak hands we put in it or the range is top-weighted. That's a different, though related, issue.

You can consistently find spots where you're an 80% favorite and your biggest problem in poker is finding out what do with when someone shows you their cards and you're a favorite?

Personally I can't believe anyone takes you, and everyone else who posts these virtually identical questions, seriously.

if youre playing poker and have a small roll and are paying bills with this money and what not then yea, flipping isnt the greatest idea. QQ is not always flipping and you may be ahead alot of times, AK obv is either flipping or behind so it depends which hand you have. anyways, play your game and if it is a lower variance game then do that. if you are playing with a bigger bankroll and can afford the roller coaster ride of variance then flip away. im in a similar situation BR wise with most money locked online and having to pay some bills with my roll but im just not a big fan of folding big hands and just usually get it in. there is nothing wrong with folding a marginally +EV hand/situation. yea you can argue that youre giving away your edge but with your limitations it may be something you have to give up until your BR and lifestyle/situation is differnet.

Good post & good article, thank-you Garick.